CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The distance on a number line from a number to 0 is the _________ of the number.

Verified step by step guidance

1. Understand that the problem is asking for a term related to the distance of a number from zero on a number line.
2. Recall that the distance from zero to any number on the number line is always a non-negative value.
3. This concept is known as the 'absolute value' of the number, which measures how far the number is from zero regardless of direction.
4. The absolute value of a number \(x\) is denoted as \(|x|\) and is defined as \(|x| = x\) if \(x \geq 0\), and \(|x| = -x\) if \(x < 0\).
5. Therefore, the correct term to fill in the blank is 'absolute value'.

Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always non-negative and is denoted by vertical bars, e.g., |x|. For example, |−3| = 3 and |5| = 5.

Number Line

A number line is a visual representation of real numbers arranged in order on a straight line, with zero at the center. Positive numbers lie to the right of zero, and negative numbers lie to the left, helping to understand concepts like distance and magnitude.

Distance in Mathematics

Distance refers to the measure of how far apart two points are. On a number line, the distance between a number and zero is the absolute value of that number, reflecting the magnitude without considering direction.